The workdone by a gas molecule in an isolated system is given by, W =α β^2 e^-x^2/(α k T), where x is the displacement, k is the Boltzmann constant…

The workdone by a gas molecule in an isolated system is given by, $\displaystyle \mathrm{W}=\alpha \beta^2 \mathrm{e}^{-\frac{x^2}{\alpha k \mathrm{~T}}}$, where $\displaystyle x$ is the displacement, $\displaystyle k$ is the Boltzmann constant and T is the temperature. $\displaystyle \alpha$ and $\displaystyle \beta$ are constants. Then the dimensions of $\displaystyle \beta$ will be :